Good afternoon Annela!!!

There is a jump of 4 terms from 26 to 6 with a total jump of -20.

Each jump is -5.

26, 21, 16, 11, 6.

Sorry wrong question. Wait.

Will look at Q13 later if no one has done them yet, as I am currently on the go and unable to focus on the question.

Candle A takes 10 hours to finish.
Candle B takes 7 hours to finish.

In 1 hour, 1/10 of candle A is gone.
In 1 hour, 1/7 of candle B is gone.

In t hours, t/10 of candle A is gone.
In t hours, t/7 of candle B is gone.

In t hours, 1 - t/10 of candle A remains.
In t hours, 1 - t/7 of candle B remains.

When Candle A is 4 times of Candle B,

1 - t/10 = 4 (1 - t/7)

Multiplying all sides by 70,

70 - 7t = 280 - 40t
33t = 210
t = 70/11
= 6 4/11 hours
= 6 hours 21.818181... min
~ 6 hours 22 min

Annela, let me know if you need further explanation.

Why do you use fraction to solve this question?

Because only rates of burning of the candles can be compared directly. These can be added or subtracted from each other easily because they can be compared directly in the same time frame of t hours.

The same ideas of using rates apply for the common question of water taps.

We can only calculate the values using the rates of water flow.

If Tap A takes 8 hours to fill up a container and Tap B takes 4 hours to fill the container, then in 1 hours, tap A alone fills up 1/8 of the container and tap B alone fills up 1/4 of the container. Together, they fill up 3/8 of the container in one hour.

If you use the primary school method of drawing blocks where 10 units of Candle A has the same total length as 7 units of Candle B, you will realise that each unit from each candle represents the fraction of the candle being burned out.

Of course, model diagrams do not work here.